Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states

TL;DR

This paper investigates the crossover behavior between directed percolation models with single and infinitely many absorbing states, revealing a universal crossover exponent and effects of diffusion on universality classes.

Contribution

It identifies the nature of the crossover between different absorbing state classes and proposes a universal crossover exponent, supported by analysis of directed Ising models and diffusion effects.

Findings

Continuous crossover with universal exponent ~1.78

Discontinuous crossover under excitatory routes

Diffusion influences the universality class assignment

Abstract

At non-equilibrium phase transitions into absorbing (trapped) states, it is well known that the directed percolation (DP) critical scaling is shared by two classes of models with a single (S) absorbing state and with infinitely many (IM) absorbing states. We study the crossover behavior in one dimension, arising from a considerable reduction of the number of absorbing states (typically from the IM-type to the S-type DP models), by following two different (excitatory or inhibitory) routes which make the auxiliary field density abruptly jump at the crossover. Along the excitatory route, the system becomes overly activated even for an infinitesimal perturbation and its crossover becomes discontinuous. Along the inhibitory route, we find continuous crossover with the universal crossover exponent $\phi\simeq 1.78(6)$, which is argued to be equal to $\nu_\|$, the relaxation time exponent of the DP universality class on a general footing. This conjecture is also confirmed in the case of the directed Ising (parity-conserving) class. Finally, we discuss the effect of diffusion to the IM-type models and suggest an argument why diffusive models with some hybrid-type reactions should belong to the DP class.